/usr/include/polymake/internal/sparse_linalg.h is in libpolymake-dev-common 3.2r2-3.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 | /* Copyright (c) 1997-2018
Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
http://www.polymake.org
This program is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by the
Free Software Foundation; either version 2, or (at your option) any
later version: http://www.gnu.org/licenses/gpl.txt.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
--------------------------------------------------------------------------------
*/
#ifndef POLYMAKE_INTERNAL_SPARSE_LINALG_H
#define POLYMAKE_INTERNAL_SPARSE_LINALG_H
#include "polymake/vector"
namespace pm {
template <typename E>
typename std::enable_if<is_field<E>::value, E>::type
det(SparseMatrix<E> M)
{
const int dim = M.rows();
if (!dim) return one_value<E>();
std::vector<int> column_permutation(dim);
copy_range(entire(sequence(0, dim)), column_permutation.begin());
E result = one_value<E>();
for (auto pivotrow=entire(rows(M)); !pivotrow.at_end(); ++pivotrow) {
if (pivotrow->empty()) return zero_value<E>();
auto pivot=pivotrow->begin();
const int pr=pivotrow.index(), pc=pivot.index(); // row and column index
result *= *pivot;
if (column_permutation[pr] != pc) {
std::swap(column_permutation[pr], column_permutation[pc]);
negate(result);
}
auto beneath=cross_direction(pivot);
++beneath;
while (!beneath.at_end()) {
// delete all elements below pivot
int r=beneath.index();
const E factor=(*beneath)/(*pivot);
++beneath;
M[r] -= factor * M[pr];
}
}
return result;
}
template <typename E>
typename std::enable_if<is_field<E>::value, SparseVector<E>>::type
reduce(SparseMatrix<E> M, SparseVector<E> V)
{
const int n_cols=M.cols();
int col=0;
for (auto pivotrow=entire(rows(M));
!pivotrow.at_end() && col < n_cols; ++pivotrow) {
if (pivotrow->empty()) continue;
auto pivot=pivotrow->begin();
const E pivotelem=*pivot;
(*pivotrow) /= pivotelem;
auto in_col = cross_direction(pivotrow->begin());
for (++in_col; !in_col.at_end(); ) {
const E factor=*in_col;
const int r2=in_col.index();
++in_col;
M.row(r2) -= (*pivotrow) * factor;
}
const E factor = V[pivot.index()];
V -= (*pivotrow) * factor;
++col;
}
return V;
}
template <typename E>
typename std::enable_if<is_field<E>::value, SparseMatrix<E>>::type
inv(SparseMatrix<E> M)
{
const int dim=M.rows();
SparseMatrix<E> L=unit_matrix<E>(dim), R=unit_matrix<E>(dim);
for (auto c=entire(cols(M)); !c.at_end(); ++c) {
if (c->empty()) throw degenerate_matrix();
auto in_col=c->begin();
auto in_row=cross_direction(in_col);
int pr=in_col.index(), pc=c.index();
const E pivotelem=*in_col;
M.row(pr) /= pivotelem; L.row(pr) /= pivotelem; ++in_col;
while (! in_col.at_end()) {
const E factor=*in_col;
int r=in_col.index(); ++in_col;
M.row(r) -= factor * M.row(pr); L.row(r) -= factor * L.row(pr);
}
++in_row;
while (! in_row.at_end()) {
R.col(in_row.index()) -= (*in_row) * R.col(pc);
M.row(pr).erase(in_row++);
}
}
R.permute_cols(attach_operation(rows(M), BuildUnary<operations::front_index>()));
return R*L;
}
template <typename E, bool ensure_nondegenerate=true>
typename std::enable_if<is_field<E>::value, Vector<E>>::type
lin_solve(SparseMatrix<E> A, Vector<E> B)
{
const int m=A.rows(), n=A.cols();
int non_empty_rows=m-n;
if (ensure_nondegenerate && non_empty_rows<0) throw underdetermined();
for (auto r=entire(rows(A)); !r.at_end(); ++r) {
const int pr=r.index();
if (r->empty()) {
if (ensure_nondegenerate && --non_empty_rows<0) throw degenerate_matrix();
if (!is_zero(B[pr])) throw infeasible();
continue;
}
auto in_row=r->begin();
auto in_col=cross_direction(in_row);
const E pivotelem=*in_row;
if (!is_one(pivotelem)) {
(*r) /= pivotelem;
B[pr] /= pivotelem;
}
for (++in_col; !in_col.at_end(); ) {
const E factor=*in_col;
const int r2=in_col.index();
++in_col;
A.row(r2) -= (*r) * factor;
B[r2] -= B[pr] * factor;
}
}
Vector<E> result(A.cols());
for (auto r=entire(reversed(rows(A))); !r.at_end(); ++r) {
if (r->empty()) continue;
typename SparseMatrix<E>::row_type::iterator in_row=r->begin();
typename SparseMatrix<E>::col_type::iterator in_col=cross_direction(in_row);
const E& elem=result[in_row.index()]=B[r.index()];
while (!(--in_col).at_end())
B[in_col.index()] -= elem * (*in_col);
}
return result;
}
} // end namespace pm
#endif // POLYMAKE_INTERNAL_SPARSE_LINALG_H
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